Simplify the following expression: $p = \dfrac{-15n^3 - 15n^2}{50n^3 - 50n^2}$ You can assume $n \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-15n^3 - 15n^2 = - (3\cdot5 \cdot n \cdot n \cdot n) - (3\cdot5 \cdot n \cdot n)$ The denominator can be factored: $50n^3 - 50n^2 = (2\cdot5\cdot5 \cdot n \cdot n \cdot n) - (2\cdot5\cdot5 \cdot n \cdot n)$ The greatest common factor of all the terms is $5n^2$ Factoring out $5n^2$ gives us: $p = \dfrac{(5n^2)(-3n - 3)}{(5n^2)(10n - 10)}$ Dividing both the numerator and denominator by $5n^2$ gives: $p = \dfrac{-3n - 3}{10n - 10}$